Would you say that other proof of work puzzles such as Cuckoo Cycle [1], which asks for a fixed length cycle in a large random bipartite graph, is a brute force

Would you say that other proof of work puzzles such as Cuckoo Cycle [1], which asks for a fixed length cycle in a large random bipartite graph, is a brute force search as well? Because that one is certainly not solved by trying all possible cycles. [1] https://github.com/tromp/cuckoo https://github.com/tromp/cuckoo